Credit new pet that crawled (5)
I believe the answer is:
crept
'that crawled' is the definition.
(I've seen this before)
'credit new pet' is the wordplay.
'credit' becomes 'cr' (abbreviation).
'new' is an anagram indicator.
'pet' with letters rearranged gives 'ept'.
'cr'+'ept'='CREPT'
(Other definitions for crept that I've seen before include "Sneaked" , "cringed" , "Moved slowly with stealth and caution" , "was obsequious" , "Moved slowly and carefully" .)